Video Sequence Reconstruction.
The overall architecture of TranSVAE follows a VAE-based structure [1]}, [2]}, [3]} with two sets of latent factors \(\mathbf {z}_1^\mathcal {D},...,\mathbf {z}_T^\mathcal {D}\)  and \(\mathbf {z}_d^{\mathcal {D}}\) .
The generative and inference graphical models are presented in Fig. REF  and REF , respectively.
Similar to the conventional VAE, we use a standard Gaussian distribution for static latent factors.
For dynamic ones, we use a sequential prior \(\mathbf {z}_t^\mathcal {D}|\mathbf {z}_{<t}^\mathcal {D} \sim \mathcal {N}(\mu _t, diag(\sigma _t^2))\) , that is, the prior distribution of the current dynamic factor is conditioned on the historical dynamic factors.
The distribution parameters can be re-parameterized as a recurrent network, e.g., LSTM, with all previous dynamic latent factors as the input.
Denoting \(\mathbf {Z}^\mathcal {D} = \lbrace \mathbf {z}_1^\mathcal {D},...,\mathbf {z}_T^\mathcal {D}\rbrace \)  for simplification, we then get the prior as follows:
\( p(\mathbf {z}_d^{\mathcal {D}},\mathbf {Z}^\mathcal {D}) = p(\mathbf {z}_d^{\mathcal {D}})\prod _{t=1}^Tp(\mathbf {z}_t^\mathcal {D}|\mathbf {z}_{<t}^\mathcal {D}).\) 
